An extension of CGAL to the oriented projective plane T2 and its dynamic visualization system

Authors:
A. G. Oliveira;P. J. de Rezende;F. P. Selmi-Dei
Affiliations:
Universidade Estadual de Campinas, Campinas, Brazil;Universidade Estadual de Campinas, Campinas, Brazil;Universidade Estadual de Campinas, Campinas, Brazil
Venue:
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Year:
2005

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Oriented projective geometry

Oriented projective geometry
An Optimal Algorithm to Construct all Voronoi Diagrams for k Nearest Neighbor Search in T2

SIBGRAPI '99 Proceedings of the XII Brazilian Symposium on Computer Graphics and Image Processing

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Abstract

The oriented projective plane T2 is an extension of the Euclidean plane E2 and comprises a number of advantages for algorithm design and implementation. We have extended the Computational Geometry Algorithms Library (CGAL) to allow for the implementation of geometric primitives and algorithms. The present video illustrates both the extension of a few algorithms to T2 under CGAL and a dynamic visualization system (T2 Viewer)built specially for displaying the spherical and planar models of T2.